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Stationary Point

When the poly...

Question

When the polynomial $5 x^{3} + m x + n$ is divided by $x^{2} + x + 1$ the remainder is $0$ . The value of $(m + n)$ is equal to (where $m, n \in R$ )

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Solution

The correct option is C $- 5$
$ω$ and $ω^{2}$ are roots of $x^{2} + x + 1 = 0$
So they are roos of $5 x^{3} + M x + N = 0$ also
third root must be 1 as sum of roots is zero and $1 + ω + ω^{2} = 0$
So the equation is $5 (x - 1) (x - ω) (x - ω^{2} = 5 (x^{3} - 1) = 0$
$⟹ M = 0 N = - 5$

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